Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways
Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways
复制标题
DOI：
10.1016/j.jtbi.2010.12.016
复制
发表时间：
2011-03-21
影响因子：
2
通讯作者：
Chaplain, Mark A. J.
中科院分区：
文献类型：
--
作者：
Sturrock, Marc;Terry, Alan J.;Chaplain, Mark A. J.
转录因子的正确定位对于许多细胞内信号通路的正常功能至关重要。实验数据表明，许多途径在时间和空间上都表现出所涉物质浓度的振荡。负反馈回路是这些振荡的重要组成部分，为所涉及的因素提供了精细的调节。本文考虑了两种这样的路径-Hes 1和p53-Mdm 2的数学模型。在以前的数学建模方法的基础上，我们推导出偏微分方程组来捕获Hes 1和p53-Mdm 2系统中变量在空间和时间上的演化。通过计算模拟，我们表明，我们的反应扩散模型能够产生持续的振荡空间和时间，准确地反映了实验证据和推进以前的模型。我们的模型的模拟还允许我们计算每个mRNA和蛋白质系统中变量的扩散系数范围，以及观察到持续振荡的模型的其他关键参数的范围。最后，通过利用偏微分方程的显式空间性质，我们还能够在数学上操纵核糖体的空间位置，从而控制蛋白质在细胞质内合成的位置。这些模拟的结果预测了一个最佳的距离以外的核蛋白质合成应该发生，以产生持续的oscillation.Using偏微分方程模型，可以获得新的信息精确的时空动态的mRNA和蛋白质。确定细胞内蛋白质空间定位的能力可能会对一系列细胞疾病如糖尿病和癌症产生新的见解。(C)2010爱思唯尔有限公司版权所有。
The correct localisation of transcription factors is vitally important for the proper functioning of many intracellular signalling pathways. Experimental data has shown that many pathways exhibit oscillations in concentrations of the substances involved, both temporally and spatially. Negative feedback loops are important components of these oscillations, providing fine regulation for the factors involved. In this paper we consider mathematical models of two such pathways-Hes1 and p53-Mdm2.Building on previous mathematical modelling approaches, we derive systems of partial differential equations to capture the evolution in space and time of the variables in the Hes1 and p53-Mdm2 systems. Through computational simulations we show that our reaction-diffusion models are able to produce sustained oscillations both spatially and temporally, accurately reflecting experimental evidence and advancing previous models. The simulations of our models also allow us to calculate a diffusion coefficient range for the variables in each mRNA and protein system, as well as ranges for other key parameters of the models, where sustained oscillations are observed. Finally, by exploiting the explicitly spatial nature of the partial differential equations, we are also able to manipulate mathematically the spatial location of the ribosomes, thus controlling where the proteins are synthesized within the cytoplasm. The results of these simulations predict an optimal distance outside the nucleus where protein synthesis should take place in order to generate sustained oscillations.Using partial differential equation models, new information can be gained about the precise spatio-temporal dynamics of mRNA and proteins. The ability to determine spatial localisation of proteins within the cell is likely to yield fresh insight into a range of cellular diseases such as diabetes and cancer. (C) 2010 Elsevier Ltd. All rights reserved.